Nilpotent group

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Nilpotent group: A group having a central series of finite length. Equivalently, a group where the upper central series terminates in finitely many steps at the whole group. Equivalently, a group where the lower central series terminates in finitely many steps at the trivial subgroup.

Term variations: Nilpotency class (also called nilpotence class).

Primary subject wiki entry: Groupprops:Nilpotent group